1. Integration of abduction and induction in biological networks using CF-induction Yoshitaka Yamamoto Graduate University for Advanced Studies Tokyo, Japan. Andrei Doncescu LAAS-CNRS Toulouse, France. Katsumi Inoue National Institute of Informatics Tokyo, Japan. FJ’07

2. Our goal Modeling of biological systems: –Explain and predict the metabolic pathway into the cell –Generic Model: Saccharomyces Cerevisiae E-coli –Inductive/Abductive Logic Programming: can explain the biological knowledge

3. 3 Outline Logical setting of abduction and induction CF-induction (CFI) Consequence finding Procedure of CF-induction Features of CF-induction Inhibition in metabolic networks Simplification of metabolic networks How enzymes work Effect on toxins Prediction for inhibition in metabolic networks Integration of abduction and induction on the inhibitory effect using CFI System demonstration Conclusion and future work 3

4. Abduction and Induction: Logical Framework Input: –B : background theory. –E : (positive) examples / observations. Output: H : hypothesis satisfying that – B  H ╞ ═ E – B  H is consistent. Inverse Entailment (IE) B E ILP machine H Computing a hypothesis H can be done deductively by: B ∧ ￢ E ╞ ═ ￢ H We use a consequence finding technique for (IE) computation.

5. Consequence finding Given an axiom set, the task of consequence finding is to find out some theorems of interest. Theorems to find out are not given in an explicit way, but are characterized by some properties. Restricted consequence finding –How to find only interesting conclusions? [Inoue 91] –Production field and characteristic clauses Production field P = – L : the set of literals to be collected – Cond : the condition to be satisfied (e.g. length) Th P ( Σ ) : the clauses entailed by Σ which belong to P. Characteristic clause C of Σ (wrt P ): – C belongs to Th P ( Σ ) ; – no other clause in Th P ( Σ ) subsumes C. Carc( Σ, P) = μ Th P ( Σ ), where μ represents “subsumption-minimal”.

6. SOLAR IE for Abduction --- SOLAR (Nabeshima, Iwanuma & Inoue 2003) B: full clausal theory E: conjunction of literals ( ￢ E is a clause) H: conjunctions of literals ( ￢ H is a clause) Example: graph completion problem – pathway finding Find an arc which enables a path from a to d. Axioms: [ ￢ node(X), ￢ node(Y), ￢ arc(X,Y), path(X,Y)]) [ ￢ node(X), ￢ node(Y), ￢ node(Z), ￢ arc(X,Y), ￢ path(Y,Z),path(X,Z)]. [node(a)]. [node(b)]. [node(c)]. [node(d)]. [arc(a,b)]. [arc(c,d)]. Negated Observation: [ ￢ path(a,d)]. Production_field: [ ￢ arc(_,_)]. SOLAR outputs four consequences: [ ￢ arc(a, d)], [ ￢ arc(a, c)], [ ￢ arc(b, d)], [ ￢ arc(b, c)] a c b d

7. IE for Induction CF-induction CF-induction (Inoue 2004: Yamamoto, Ray & Inoue 2007) fc-HAIL fc-HAIL (Inoue & Ray 2007) B, E, H: full clausal theory Note: CF-induction is the only existing ILP system that is complete for full clausal theories.

8. B ∧ ￢ E ⊨ ￢ H (IE) ⇔ B ∧ ￢ E ⊨ Carc(B ∧ ￢ E, P) ⊨ ￢ H. CC ⊨ ￢ H where CC ⊆ Instances(Carc(B ∧ ￢ E, P)). H ⊨ F where F is ￢ CC in CNF. Principle of CF-induction Algorithm 1.Compute Carc(B ∧ ￢ E, P). 2.Construct a bridge formula CC. 3.Convert ￢ CC into CNF F. 4.Generalize F to H such that B ∧ H is consistent; H is Skolem-free. ＊ Generalization H ⊨ F － inverse Skolemization － anti-instantiation － dropping literals from clauses － addition of clauses － inverse resolution － Plotkin’s least generalization

9. 9 Outline Logical Setting of Abduction and Induction CF-induction (CFI) Consequence finding Procedure of CF-induction Features of CF-induction Inhibition in metabolic networks Simplification of metabolic networks How enzymes work Effect on toxins Prediction for inhibition in metabolic networks Integration abduction and induction on the inhibitory effect using CFI System demonstration Conclusion and future work

10. Simplification of metabolic networks Metabolic pathway : sequences of enzyme-catalyzed reaction steps, converting substrates to a variety of products to meet the needs of the cell. Mono-molecular enzymes catalyzed reactions: mediated by enzymes—proteins that encourage a chemical change. Enzymes: accelerate the rate of a chemical reaction by up to three orders of magnitude E : enzyme, S : substrate, P : product, ES : complex, k : the constant of the rate of a chemical reaction. E + SESE + P k1k1 k- 1 k2k2 k- 2 EE S ES P

11. 11 How enzymes work Activity of an enzyme: - the rate of the chemical reaction catalyzed by the enzyme. - 1 unit (U) ≡ the amount of the enzyme for changing the substrate whose amount is 1 μmol to the product over one minute. - proportionate to the amount of the enzyme. Michaelis-Menten Reaction: - the relation between the activity of an enzyme and the concentration of a substrate - at steady state Concentration of substrate Time [T] Activity Concentration of Enzyme E + S ESE + P k1 k-1 k2 k-2 V = k 2 [ES] - k -2 [E][P] V = V max K m + [S] [S] V Vmax

12. 12 Effect on toxins There exists chemical compounds (inhibitors) which control activities of enzymes. Higher the concentration of a inhibitor is, lower the activity of the enzyme controlled by the inhibitor becomes. E E E S P S I I S I Activity Concentration of substrate —: without inhibitor —: with inhibitor E I

13. 13 Logical modeling of inhibition [Tamaddoni-Nezda et al 2006] Enz SP Toxin Inhibited Enz SP Toxin Not inhibited Enz SP Toxin Not inhibited concentration(P, down) ← reaction(S, Enz, P), ￢ inhibited(Enz, S, P), concentration(S, down). concentration(P, up) ← reaction(S, Enz, P), ￢ inhibited(Enz, S, P), concentration(S, up). concentration(P, down) ← reaction(S, Enz, P), inhibited(Enz, S, P). concentration(S, up) ← reaction(S, Enz, P), inhibited(Enz, S, P).

14. 14 Prediction for inhibitory effect of a toxin Examples E : changes (up or down) of concentrations of metabolites in treated cases (injected with a toxin) Background Theory B : - chemical reactions in a metabolic networks - four clauses concerning the inhibitory effect of a toxin Hypothesis H : a conjunction of literals whose predicate is “inhibition” The goal - Finding inhibitions of a metabolic pathway Our approach - Using IE for abduction

15. Example 1/2 2-oxe-glutarate l-lysinel-2-aminoadipate isocitrate trans-aconitatecitrate fumaratetaurinesuccinate nmndnmnahippurate acryloyl-coa formate formaldehydesarcosine l-ascitrulline ornithinearginine urea creatine creatinine methylamine tmao lactate beta-alanine 2.6.1.39; 4.2.1.36;... 1.2.1.31; 1.5.1.7;... 4.3.2.1 3.6.3.3

16. Example 2/2 2-oxe-glutarate l-lysinel-2-aminoadipate isocitrate trans-aconitatecitrate fumaratetaurinesuccinate nmndnmnahippurate acryloyl-coa formate formaldehydesarcosine l-ascitrulline ornithinearginine urea creatine creatinine methylamine tmao lactate beta-alanine 2.6.1.39; 4.2.1.36;... 1.2.1.31; 1.5.1.7;... 4.3.2.1 3.6.3.3

17. 17 Outline Logical Setting of Abduction and Induction CF-induction (CFI) Consequence finding Procedure of CF-induction Features of CF-induction Inhibition in metabolic networks Simplification of metabolic networks How enzymes work Effect on toxins Prediction for inhibition in metabolic networks Integration abduction and induction on the inhibitory effect using CFI System demonstration Conclusion and future work 17

18. Goals - Predicting the concentration of metabolites intracellular - Discovering inductive rules augmenting incomplete background theory Our Approaches - Using CF-induction Prediction for intracellular fluxes Examples E : changes (up or down) of concentrations of metabolites extracelluar Background theory B : - chemical reactions in a metabolic networks - two clauses concerning the inhibitory effect Hypothesis H : - a clausal theory which consists of both lierals whose predicate is “inhibition” and clauses corresponding to inductive rules

19. 19 Metabolite Balancing Intracellular fluxes are determined as a function of the measurable extracellular fluxes using a stoichiometric model for major intracellular reactions and applying a mass balance around each intracellular metabolite. v1, v2, v3+, v3-, v4 : unknown fluxes at the steady state. rA, rC, rD, rE : metabolite extracellular accumulation rate.

20. E : concentration(d, up). concentration(e, down). concentration(c, down). B : concentration(a, up). reaction(a, b). reaction(b, d). reaction(d, e). reaction(e, c). reaction(c, b). reaction(b, c). ￢ concentration(X, up) ← concentration(X, down). concentration(X, up) ← concentration(Y, up), reaction(Y, X), reaction(X, Z), ￢ inhibited(Y, X), inhibited(X, Z). concentration(X, down) ← reaction(Y, X), ￢ inhibited(Y, X), concentration(Y, down). Example 1: YXYXZ

21. H 2 : ￢ inhibited(a, b). inhibited(b, c). ￢ inhibited(b, d). inhibited(d, e). concentration(X, down) ← concentration(Y, up), inhibited(Y, X). H 1 : ￢ inhibited(a, b). inhibited(b, c). ￢ inhibited(e, c). inhibited(d, e). ￢ inhibited(b, d). concentration(e, down) ← inhibited(d, e), ￢ inhibited(e, c). Example 1: outputs of CF-induction de c YX

22. Example 2: the real metabolic pathway (Pyruvate) B: reaction(pyruvate, acetylcoa). reaction(pyruvate, acetaldehide). reaction(glucose, glucosep). reaction(glucosep, pyruvate). reaction(acetaldehide, acetate). reaction(acetate, acetylcoa). reaction(acetaldehide, ethanol). concentration(glucose, up). terminal(ethanol). blocked(X)←reaction(X,Z), inhibited(X,Z). blocked(X)←terminal(X). concentration(X,up) ←reaction(Y,X), ￢ inhibited(Y,X), blocked(X). E : concentration(ethanol,up). concentration(pyruvate, up). Acetate AcetaldehidePyruvate Glucose-P Ethanol Glucose Acetylcoa EC 4.1.1.1 EC 1.1.1.1 EC 1.2.1.10EC 1.2.4.1 X Z X

23. H 1 : ￢ Inhibited(glucosep, pyruvate). ￢ inhibited(acetaldehide, ethanol). inhibited(pyruvate, acetylcoa). Example 2: outputs of CF-induction Ethanol Acetate AcetaldehidePyruvate Glucose-P Glucose Acetylcoa Acetate AcetaldehidePyruvate Glucose-P Glucose Acetylcoa Ethanol H 2 : ￢ inhibited(glucose, glucosep) ￢ Inhibited(glucosep, pyruvate). ￢ inhibited(acetaldehide, ethanol). ￢ inhibited(pyruvate, acetaldehide). concentration(Y, up)← ￢ inhibited(X, Y), concentration(X, up).

24. 24 E : concentration(d, up). concentration(e, down). concentration(c, down). B : concentration(a, up). reaction(a, b). reaction(b, d). reaction(d, e). reaction(e, c). reaction(c, b). reaction(b, c). ￢ concentration(X, up) ← concentration(X, down). concentration(X, up) ← concentration(Y, up), reaction(Y, X), reaction(X, Z), ￢ inhibited(Y, X), inhibited(X, Z). concentration(X, down) ← reaction(Y, X), ￢ inhibited(Y, X), concentration(Y, down). YXYXZ H 1 : ￢ inhibited(a, b). inhibited(b, c). ￢ inhibited(e, c). inhibited(d, e). ￢ inhibited(b, d). concentration(e, down) ← inhibited(d, e), ￢ inhibited(e, c). de c

25. Conclusion Introduction of inhibitions in metabolic pathways Introduction of CF-induction Full clausal theories (non-Horn clauses) for B, E and H Completeness of hypotheses finding Integration of abduction and induction on inhibitory effects using CF-induction.